Suppose f: A --> B is a function. We call g: B --> A the inverse of f if g composed with f is the identity map on A (denoted by IdA) and f composed with g is IdB. Please solve the screenshot, thank you! 1. Show that the inverse of a function is unique. If a function has aninverse, then it only has one.2. Suppose f : A → B and g : B → C have inverses. Show that gof isinvertible, and that its inverse is f-l og¬1.

Solution:(1)Let f:A→B be an invertible function, we have toshow that it's inverse is unique.…

Answered: 1. Show that the inverse of a function…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose f: A --> B is a function. We call g: B --> A the inverse of f if g composed with f is the identity map on A (denoted by Id_A) and f composed with g is Id_B. Please solve the screenshot, thank you!

1. Show that the inverse of a function is unique. If a function has an
inverse, then it only has one.
2. Suppose f : A → B and g : B → C have inverses. Show that gof is
invertible, and that its inverse is f-l og¬1.

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